Analytical Solution of the Bloch NMR Flow Equations for the Analysis of Blockage in a Radially Symmetric Cylindrical Pipe

Abstract

The use of various types of wave energy as a probe is an increasingly promising non destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires a detailed understanding of how signals evolve in the medium of interest in the absence of inhomogeneities (obstructions or perturbation) and the nature of the emerging signal when the original signal is perturbed by obstructions that might exist in the medium. Properties of the signal are then used to estimate the level of inhomogeneity in the medium. In this study, Magnetic Resonance Imaging (MRI) is used to detect partial blockage of fluid in a cylindrical pipe. The Bloch NMR flow equation is solved analytically in cylindrical coordinates for flow of fluid in a radially symmetric cylindrical pipe. Based on the appropriate boundary conditions, the radial axis was varied to depict free flow and partial blockage in the pipe. The Nuclear Magnetic Resonance (NMR) signals obtained were then analyzed and used to provide information on the type of blockage in the cylindrical pipe.